### Nuprl Lemma : simple-comb2-classrel

`∀[Info,A,B,C:Type]. ∀[f:A ─→ B ─→ C]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].`
`  uiff(v ∈ λa,b.lifting2(f;a;b)|X;Y|(e);↓∃a:A. ∃b:B. ((a ∈ X(e) ∧ b ∈ Y(e)) ∧ (v = (f a b) ∈ C)))`

Proof

Definitions occuring in Statement :  simple-comb2: `λx,y.F[x; y]|X;Y|` classrel: `v ∈ X(e)` eclass: `EClass(A[eo; e])` event-ordering+: `EO+(Info)` es-E: `E` uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` exists: `∃x:A. B[x]` squash: `↓T` and: `P ∧ Q` apply: `f a` function: `x:A ─→ B[x]` universe: `Type` equal: `s = t ∈ T` lifting2: `lifting2(f;abag;bbag)`
Lemmas :  simple-comb-classrel false_wf le_wf select_wf cons_wf nil_wf sq_stable__le length_wf length_nil non_neg_length length_wf_nil length_cons length_wf_nat int_seg_wf decidable__equal_int subtype_base_sq int_subtype_base lelt_wf lifting2_wf bag_wf classrel_wf simple-comb2_wf squash_wf exists_wf es-E_wf event-ordering+_subtype event-ordering+_wf eclass_wf all_wf bag-member_wf bag-member-single single-bag_wf bag-combine_wf bag-member-combine simple-comb_wf less-iff-le add-swap le-add-cancel2 add-associates minus-zero minus-add add-commutes condition-implies-le le-add-cancel add-zero zero-add add_functionality_wrt_le not-equal-2 and_wf es-interface-subtype_rel2 equal_wf

Latex:
\mforall{}[Info,A,B,C:Type].  \mforall{}[f:A  {}\mrightarrow{}  B  {}\mrightarrow{}  C].  \mforall{}[X:EClass(A)].  \mforall{}[Y:EClass(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].
\mforall{}[v:C].
uiff(v  \mmember{}  \mlambda{}a,b.lifting2(f;a;b)|X;Y|(e);\mdownarrow{}\mexists{}a:A.  \mexists{}b:B.  ((a  \mmember{}  X(e)  \mwedge{}  b  \mmember{}  Y(e))  \mwedge{}  (v  =  (f  a  b))))

Date html generated: 2015_07_22-PM-00_10_48
Last ObjectModification: 2015_01_30-AM-01_48_48

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